Counting Techniques Question

Question

How many seven-digit telephone numbers can be made if the first three digits must be different

and the number cannot start with “0”?

I'm having some trouble with this question, can someone please explain how to do this? It would be very helpful, and for these type of questions how would you know if the elements can be repeated or not?

Answer 1

I shall present my solution once more.

1st #: 9 choices (zero is excluded)

2nd #: 9 choices (1st number excluded, zero added)

3rd #: 8 choices (1st and 2nd number excluded)

Numbers may be repeated for the next four places

4th, 5th, 6th, and 7th, all have 10 choices

(9)(9)(8)(10)(10)(10)(10) = ?

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